3 ms·

Math is merely a mutual agreement. First an agreement on root principles, and then an agreement on notation for these root principles. The rest is built on top

by tabtab 3y ago

Math is merely a mutual agreement. First an agreement on root principles, and then an agreement on notation for these root principles. The rest is built on top of those. Nobody is forced to accept the premises. (Unless you don't want an F in math class.)

dekhn 3y ago
One imagines two intelligent alien races would be able to communicate that pi is the ratio of the circumference to the diameter of a circle without coming to any real agreements over postulates or axioms. But I suppose that's natural philosophy, not math. See https://computingbiology.github.io/docs/hamming1998.pdf https://computingbiology.github.io/docs/hamming1998.pdf "Mathematics on a Distant Planet" for more thinking. Many physicists think that math is instrinsic and absolute (objective) in the universe, not "merely a mutual agreement"
- proamdev123 3y ago
  > One imagines two intelligent alien races would be able to communicate that pi is the ratio of the circumference to the diameter of a circle without coming to any real agreements over postulates or axioms. Except circles don’t exist in the real world. They are an abstraction that mankind created that are similar enough to many natural objects as to be a useful abstraction of them. In order for two alien races to communicate about pi, they’d have to first agree on the definition of a circle as a set of points equidistant from a central point. That’s one of the axioms they’d have to agree on before they could even get to pi.
  - jaza 3y ago
    Assuming that the two alien races are indeed "intelligent" (approximately relative to humans), and that they possess sensory perceptors approximately similar to those of humans, and that they inhabit the same observable universe as humans do - a universe that contains a great many physical (imperfect) circles - surely they should be expected to have conceived of the same abstraction of a (perfect) circle? And therefore to have gotten to pi? Then again, maybe a circle (and all other geometric abstractions) are too tied specifically to visual perception. Maybe, for example, intelligent aliens who only have auditory perception, would have no concept of a circle but would have gotten to the Doppler effect. Or intelligent aliens who only have tactile perception, would have no concept of a circle but would have gotten to the laws of thermodynamics.
dalmo3 3y ago
I'm just glad Curiosity and Mars reached a mutual agreement on their trajectories.
- tabtab 3y ago
  Agreement is not to be taken for granted: https://www.wired.com/2010/11/1110mars-climate-observer-report/ https://www.wired.com/2010/11/1110mars-climate-observer-repo...
grumbel 3y ago
How do you agree on those root principles? Don't you need a set of even lower level shared rules and ability that allows you to agree on anything in the first place? If I show the paper with the rules to a dog, I don't think they can agree or disagree with me in any meaningful way, despite otherwise being reasonably intelligent creatures. Could there be aliens that are vastly different from us that can make rules that we would be unable to agree to? Could there be aliens similar to us, that would have different means to agree that are incompatible with ours?

by tabtab 3y ago

dekhn 3y ago

One imagines two intelligent alien races would be able to communicate that pi is the ratio of the circumference to the diameter of a circle without coming to any real agreements over postulates or axioms. But I suppose that's natural philosophy, not math. See https://computingbiology.github.io/docs/hamming1998.pdf https://computingbiology.github.io/docs/hamming1998.pdf "Mathematics on a Distant Planet" for more thinking. Many physicists think that math is instrinsic and absolute (objective) in the universe, not "merely a mutual agreement"

proamdev123 3y ago
> One imagines two intelligent alien races would be able to communicate that pi is the ratio of the circumference to the diameter of a circle without coming to any real agreements over postulates or axioms. Except circles don’t exist in the real world. They are an abstraction that mankind created that are similar enough to many natural objects as to be a useful abstraction of them. In order for two alien races to communicate about pi, they’d have to first agree on the definition of a circle as a set of points equidistant from a central point. That’s one of the axioms they’d have to agree on before they could even get to pi.
- jaza 3y ago
  Assuming that the two alien races are indeed "intelligent" (approximately relative to humans), and that they possess sensory perceptors approximately similar to those of humans, and that they inhabit the same observable universe as humans do - a universe that contains a great many physical (imperfect) circles - surely they should be expected to have conceived of the same abstraction of a (perfect) circle? And therefore to have gotten to pi? Then again, maybe a circle (and all other geometric abstractions) are too tied specifically to visual perception. Maybe, for example, intelligent aliens who only have auditory perception, would have no concept of a circle but would have gotten to the Doppler effect. Or intelligent aliens who only have tactile perception, would have no concept of a circle but would have gotten to the laws of thermodynamics.

dalmo3 3y ago

I'm just glad Curiosity and Mars reached a mutual agreement on their trajectories.

tabtab 3y ago
Agreement is not to be taken for granted: https://www.wired.com/2010/11/1110mars-climate-observer-report/ https://www.wired.com/2010/11/1110mars-climate-observer-repo...

grumbel 3y ago

How do you agree on those root principles? Don't you need a set of even lower level shared rules and ability that allows you to agree on anything in the first place? If I show the paper with the rules to a dog, I don't think they can agree or disagree with me in any meaningful way, despite otherwise being reasonably intelligent creatures. Could there be aliens that are vastly different from us that can make rules that we would be unable to agree to? Could there be aliens similar to us, that would have different means to agree that are incompatible with ours?